Actually, it is amazing that the simple idea of dropping serifs at the ends of strokes didn't occur to the great many typographers who experimented with their shapes and sizes so much. In part, it is due to the inertia of scribes' tradition who, with their quills, simply could not produce a reasonably clean cut of a stroke. Undoubtedly, old typographers also knew the fact that was later confirmed by experiments: Serifs help the eye to stick to the line and thus facilitate reading.
But the biggest part of the serif persistence was, of course, due to plain habit. When the first examples of sans serif fonts finally appeared, they seemed so controversial that the first name given to them was "grotesque," and they were very rarely used except in advertising. And so it remained until the newest trends in art and industrial design, most notably the German Bauhaus movement of 1920s (influenced by earlier Russian constructivism), required adequate means of typographic expression. These movements stressed utilitarian aspects in design, claiming that a thing becomes beautiful only when---and because---it serves a practical purpose, denying any attempts to artificially "adorn" it.
The most influential type design of that epoch, the Futura font created in Germany in 1928, displayed the core of the Bauhaus ideology: strictly geometric outline, lacking any embellishments and just barely conforming to the historical shapes of letters. The resulting blend of geometric consistency and aesthetic awkwardness may be disputable, but it was at least something quite new, and therefore impressive, at that time. Now we're much more accustomed to the look of Futura (and its many derivatives), but the inborn radicalism of the font still shows through.
As any other radical movement, the "new sans serif" typography of the 1920s couldn't do without auguring an imminent death of all serif fonts whatsoever. This didn't happen, of course. Moreover, Futura itself didn't manage to become so neutral and familiar in the mass perception as to become a standard sans serif font for all occasions. (Instead, this position was taken by Helvetica, a typical "no-nonsense," "no-big-deal" font that became ubiquitous almost to the point of being misused and nauseating.) However, it cannot be denied that Futura played an important role in sans serif becoming a mainstream type style, an accepted contrasting pair for the time-proven serif fonts.
Of course, sans serif proliferation was also due to the higher demand for display typefaces in all media, the demand which is much more severe than at any time in the past. The most natural use of a sans serif font is still for display purposes (ads, titles, logos, labels of all sorts), although it can be successfully used for body text as well.
It is interesting to note that the development of sans serif typefaces in this century went in a direction opposite to that of the serif type development of previous centuries. Indeed, we've seen how serif faces have gone from arty and liberal Old Style, through neutral Transitional design, to the rigid, mannered Modern typefaces. Conversely, sans serif fonts started from Futura with its artificial look, then were for a long time dominated by neutral "transitional" Helvetica, and recently a number of distinctively liberal (and, in some classifications, even termed "humanist") sans serif faces became popular. Thus, the 20th century process of sans serif humanization is a negation, a mirror image, a contrasting parallel for the earlier process of serif dehumanization in 15th-19th centuries---just as sans serif itself is a contrasting match for serif.
So what are the features of humanist sans serif faces? One of the first such designs was Frutiger (a.k.a. Freeset, developed in 1976); at first sight similar to Helvetica, this font reveals to a careful investigation some "anti-geometric" features, such as uneven width of strokes (especially in bold variants), non-perpendicular cuts, and slightly bent off tips of strokes (e.g. the bottom of the vertical stroke in "d"). All these subtleties were intended to smooth out the too harsh edges of the generic sans serif design and improve legibility of characters, and their net result is a relatively warm and friendly-looking typeface---especially if we compare it to the apathetic Helvetica or phrenetic Futura.
The trends that were hinted at in Frutiger were later fully developed in a family of fonts now extremely popular both on the Web and in print design. The original typeface of this family, called Meta, was developed in 1984 by German designer Erik Spiekermann. In Meta and its offsprings, strokes have slightly varying width (the creator's goal was that in small sizes, thinner strokes should not "drop out" but, on the contrary, become undistinguishable from the thicker ones) and, in compensation for the missing serifs, vigorously bent-off tips of vertical strokes in letters like "d" or "n." Both uppercase and lowercase characters are narrower than in most other sans serif fonts (i.e. letters are inscribed into rectangles, not squares). Perhaps here we have an example showing how far can we go in "humanizing" sans serifs and borrowing serif-specific features, while remaining within the sans serif paradigm.
Interestingly, the problems that the designer tried to resolve with the new typeface were purely practical---Spiekermann's goal was to create an economic font readable in a wide variety of sizes and conditions. Here's what the designer himself writes in his article: Meta has been hailed as "the typeface for the nineties"; young designers seem to appreciate its rugged charm, which owes a lot to the detailed requirements of small type on bad paper. It was never designed to be a trendy typeface, rather it was designed to solve specific problems. Maybe it is that honest, unpretentious background which appeals to graphic designers and typographers around the world.
Here's a truly enlightening comparison: Note how the two approaches to a "purely utilitarian" font design, differing only by the fact that one was rather theoretic and the other driven by practical needs, resulted in two fonts as different as Futura and Meta.